Journal Articles SIAM Journal on Matrix Analysis and Applications Year : 2024

Communication Lower Bounds and Optimal Algorithms for Multiple Tensor-Times-Matrix Computation

Abstract

Multiple Tensor-Times-Matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. We establish communication lower bounds that determine how much data movement is required (under mild conditions) to perform the Multi-TTM computation in parallel. The crux of the proof relies on analytically solving a constrained, nonlinear optimization problem. We also present a parallel algorithm to perform this computation that organizes the processors into a logical grid with twice as many modes as the input tensor. We show that with correct choices of grid dimensions, the communication cost of the algorithm attains the lower bounds and is therefore communication optimal. Finally, we show that our algorithm can significantly reduce communication compared to the straightforward approach of expressing the computation as a sequence of tensor-times-matrix operations when the input and output tensors vary greatly in size.
Fichier principal
Vignette du fichier
multi-TTM.pdf (627) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-03950359 , version 1 (21-01-2023)

Licence

Identifiers

Cite

Hussam Al Daas, Grey Ballard, Laura Grigori, Suraj Kumar, Kathryn Rouse. Communication Lower Bounds and Optimal Algorithms for Multiple Tensor-Times-Matrix Computation. SIAM Journal on Matrix Analysis and Applications, 2024, 45 (1), pp.450-477. ⟨10.1137/22M1510443⟩. ⟨hal-03950359⟩
146 View
105 Download

Altmetric

Share

More